1. Field of the Invention
The present invention relates to an apparatus for processing &uzzy information based on fuzzy logic.
2. Description of the Prior Art
In conventional fuzzy information processing, membership functions are represented in two-dimensional space, one axis of which is input variable x and the other is its grade of compatibility or degree t of membership with respect to a fuzzy set. Therefore the method, in case of processing more than two input variables x.sub.1, x.sub.2, . . . , derives the totally evaluated grade by the composition of all grades t.sub.1, t.sub.2, . . . , each of which is obtained from a membership function defined on each input variable. We call this kind of membership function a "conventional type".
An example of the case in which two input variables exist is shown in FIGS. 1 and 2. For input variables x and y conventional type membership functions M.sub.x and M.sub.y are defined, and grades t.sub.x and t.sub.y of compatibility are obtained respectively. In the figures, each membership function is given as isosceles triangle, which is often used in a fuzzy control. According to fuzzy reasoning, values of the input variables x and y are evaluated by obtaining grades t.sub.x and t.sub.y by the membership functions M.sub.x and M.sub.y as antecedents of a fuzzy "if-then" rule. Applying composition operation, usually minimum operation, to t.sub.x and t.sub.y, then the total grade of compatibility or membership value or grade of membership of the input is derived.
In general the resulting membership function for two or more input variables is constructed by composing all membership functions. The composed membership function defines a figure in space, axes of which are input variables and grade of compatability. In the case of above example, the figure is a quadrangular pyramid. And the intercept of the resulting membership function at a certain grade, that is a equigrade contour line, is interpreted as a boundary curve of a fuzzy set or a fuzzy region represented by the membership function. When fuzzy information processing is done by the conventional method, the boundary curve is limited to a particular shape depending on the composition operation. In the case of above example, it is always a rectangle in the two-dimensional plane of each input variable.
However, this limitation of boundary shape means that the shape of fuzzy set in space defined by the input variables is also limited. Therefore, the conventional multi-input system which processes fuzzy information cannot treat any fuzzy set without the predefined particular shape, characteristic of the composed membership function.
Thinking about the practical control field, a relationship between two variables are often represented by a distribution of points, of which coordinates are the values of input variables, in the two-dimensional plane of input variables. In general, it is difficult to determine the trend of distribution such as linearity or the direction of gradient, by using statistical methods. However, human judgment is rather useful to do these steps. Human judgment does not use the linear shape of distribution such as a rectangle, but extrapolates a curved shape such as a ellipse as' a clue. Fuzzy theory is thought to be able to make such judgments Therefore, it is desired that a fuzzy set which has an arbitrary boundary shape, such as an ellipse, could be incorporated into the space defined by input variables. By using the conventional method, such requirement is satisfied by approximation. That is, at first the region which is given by the above stated boundary is partitioned into smaller ones for each input variable. A conventional type membership function must be assigned to each region. Moreover, an appropriate value is assigned to the consequent of "if-then" type production rule.
However, such processing method has the following problems.
(1) It needs a great number of membership functions and rules.
(2) It is difficult to recognize the shape of partitioned regions.
(3) It can only approximately incorporate fuzzy sets with varying shapes of boundaries.
(4) The processing becomes very complex in the case where there is an overlapping of more than two regions of arbitrary shape.
Because of the above mentioned reasons, the conventional fuzzy information processing method could not incorporate a fuzzy set with unlimited shape of boundary.